This invention relates to optimization of a flight route of an aircraft in an environment with constant or variable winds.
Commercial and private aircraft travel great distances, 500 to 5,000 miles, at varying altitudes and are subjected to winds up to 100 knots (120 miles per hour) in varying directions. Over the course of a long flight, requiring several hours to complete, the aircraft may change course and/or change altitude to avoid a heavy storm or a second aircraft that is climbing through the first aircraft""s present cruise altitude. Even if the aircraft cruises at a fixed altitude, the prevailing winds will vary strongly in magnitude and direction from one along the route. For typical wind patterns encountered across the North American continent (e.g., in a flight from New York to San Francisco), traveling a wind-optimized flight route can reduce flight time, relative to flight time over a great circle route, by up to 8 percent. For a flight from the JFK Airport in New York to the San Francisco Airport, this reduction in time can be 20 minutes or more. For shorter flights, the aircraft flight speed, the wind speed and wind shear are also lower and the relative effect of variable local winds is stronger, and the ratio of time required to travel a great circle route and time required to travel an optimized route is approximately constant.
However, computation from first principles of an optimal flight route between first and second waypoints in the presence of variable, even piecewise linear, wind direction and speed requires complex calculations involving many variables and may require too much time to be practical. What is needed is a less complex approach that provides a near-optimal flight route and that can compensate for the changing wind conditions encountered by an aircraft in flight. Preferably, the approach should allow use of raw numerical data or of analytical approximations for wind speed and direction encountered along a flight path and should allow for variable aircraft speed and altitude along the flight path.
These needs are met by the invention, which begins with a nominal solution that satisfies the source and destination waypoint constraints and applies a neighboring optimal control (xe2x80x9cNOCxe2x80x9d) and guidance analysis to a wind velocity vector field and aircraft speed prescription and provides a near-optimal flight route, which does not require huge computation times or a supercomputer to perform the analysis. The NOC analysis uses a feed-forward and linear feedback procedure for computing a near-optimum route at the wind velocity vector changes along the route. The computations are performed for dimensionless variables so that a given NOC solution can be applied to many other problems through appropriate scaling.